Gather a spring of spring constant 15 N, a hanging mass set, and a stopwatch.
Hang the spring off of a ring stand and attach a mass of .5 kg to the spring. Pull the spring down to an amplitude of .06 m from the equilibrium point and record the amount of time it takes to complete 10 oscillations. Divide that time by 10 to determine a single period.
Repeat step 3 for masses of .7kg, .9kg, 1.1 kg, and 1.3 kg. Keep everything else constant.
Repeat step 3 with everything remaining constant, except change the amplitudes to .03 m, .09m, 1.2m and 1.5m.
Data: Mass vs. Period:
Mass (kg)
Amplitude (m)
Period (s)
.5
.06
.63
.7
.06
.74
.9
.06
.82
1,1
.06
.90
1.3
.06
1.01
There is a strong positive, linear correlation between mass and period. The linear fit equation is y=.46x + .406 where x is the mass and y is the period. This is indicated by the r^2 value of .9958. As mass increases, the period increases. The actual equation for period for an oscillating spring is period = 2pi x square root(mass/k). Therefore, as the square root of the mass increases, then the period must also increase.
Amplitude vs. Period:
Mass(kg)
Amplitude (m)
Period (s)
.7
.03
.70
.7
.06
.70
.7
.09
.71
.7
1.2
.71
.7
1.5
.71
There is a weak, positive correlation between amplitude and period. However, the r^2 value is only .4599, so it is a stretch to even call it a correlation. The linear fit of y= .0052x+.703 is not a good fit. This is because the actual equation for the period of an oscillating spring, period = 2pi x square root(mass/k) is independent of amplitude. Therefore, the amplitude does not affect the period. There is no relationship between amplitude and period.
Procedure:
- Gather a spring of spring constant 15 N, a hanging mass set, and a stopwatch.
- Hang the spring off of a ring stand and attach a mass of .5 kg to the spring. Pull the spring down to an amplitude of .06 m from the equilibrium point and record the amount of time it takes to complete 10 oscillations. Divide that time by 10 to determine a single period.
- Repeat step 3 for masses of .7kg, .9kg, 1.1 kg, and 1.3 kg. Keep everything else constant.
- Repeat step 3 with everything remaining constant, except change the amplitudes to .03 m, .09m, 1.2m and 1.5m.
Data:Mass vs. Period:
There is a strong positive, linear correlation between mass and period. The linear fit equation is y=.46x + .406 where x is the mass and y is the period. This is indicated by the r^2 value of .9958. As mass increases, the period increases. The actual equation for period for an oscillating spring is period = 2pi x square root(mass/k). Therefore, as the square root of the mass increases, then the period must also increase.
Amplitude vs. Period:
There is a weak, positive correlation between amplitude and period. However, the r^2 value is only .4599, so it is a stretch to even call it a correlation. The linear fit of y= .0052x+.703 is not a good fit. This is because the actual equation for the period of an oscillating spring, period = 2pi x square root(mass/k) is independent of amplitude. Therefore, the amplitude does not affect the period. There is no relationship between amplitude and period.